The exponential distribution can be used to model the time until an event occurs, or the time between two events.
Examples of quantities that can be modeled using the exponential distribution are:

The time between phone calls in a call center.

The time until a machine fails.

The exponential distribution is related to the
The Poisson Distribution.
Where the Poisson distribution models the number of occurrences of an event in a specified time
span, the exponential distribution models the time between these occurrences. The probability of an event is assumed
to be constant.

The exponential distribution has one parameter, usually denoted by the Greek letter (mu). When the time until
failure is being modeled, specifies the mean time to failure. When the time between events is being modeled, then
specifies the mean time between two occurrences. This parameter acts as a scale parameter of the distribution.

The probability density function (PDF) of the exponential distribution is:

The exponential distribution is implemented by the ExponentialDistribution class. It has two
constructors. The first constructor has one parameter: the scale parameter of the distribution. The following
constructs an exponential distribution with waiting time (scale parameter) 7.6:

No code example is currently available or this language may not be supported.

let exponential = ExponentialDistribution(7.6)

If a variable is assumed to have an exponential distribution, then the parameter of the distribution can be
estimated using the method of maximum likelihood, which gives the same results as the method of matching moments. The
second constructor performs this calculation. It takes one argument: a VectorT whose distribution is to be estimated.

Note that parameter estimation says nothing about how well the estimated distribution fits the variable's
distribution. Use one of the goodness-of-fit tests to verify the appropriateness of the choice of distribution.

The ExponentialDistribution class has one specific property, ScaleParameter, which returns the
scale parameter of the distribution. This parameter commonly corresponds to the average waiting time until an event
occurs.

ExponentialDistribution has one static (Shared in Visual Basic) method, Sample, which
generates a random sample using a user-supplied uniform random number generator.